Certainty

First published Sat Feb 2, 2008

Like knowledge, certainty is an epistemic property of beliefs.
(In a derivative way, certainty is also an epistemic property of
subjects: S is certain that p just in case
S's belief that p is certain.) Although
some philosophers have thought that there is no difference between
knowledge and certainty, it has become increasingly common to
distinguish them. On this conception, then, certainty is either
the highest form of knowledge or is the only epistemic property
superior to knowledge. One of the primary motivations for
allowing kinds of knowledge less than certainty is the widespread sense
that skeptical arguments are successful in showing that we rarely or
never have beliefs that are certain (see Unger 1975 for this kind of
skeptical argument) but do not succeed in showing that our beliefs are
altogether without epistemic worth (see, for example, Lehrer 1974,
Williams 1999, and Feldman 2003; see Fumerton 1995 for an argument that
skepticism undermines every epistemic status a belief might have; and
see Klein 1981 for the argument that knowledge requires certainty,
which we are capable of having).

As with knowledge, it is difficult to provide an uncontentious
analysis of certainty. There are several reasons for this.
One is that there are different kinds of certainty, which are easy to
conflate. Another is that the full value of certainty is
surprisingly hard to capture. A third reason is that there are
two dimensions to certainty: a belief can be certain at a moment or
over some greater length of time.

There are various kinds of certainty. A belief is
psychologically certain when the subject who has it is
supremely convinced of its truth. Certainty in this sense is
similar to incorrigibility, which is the property a belief has
of being such that the subject is incapable of giving it up. But
psychological certainty is not the same thing as incorrigibility.
A belief can be certain in this sense without being incorrigible; this
may happen, for example, when the subject receives a very compelling
bit of counterevidence to the (previously) certain belief and gives it
up for that reason. Moreover, a belief can be incorrigible
without being psychologically certain. For example, a mother may
be incapable of giving up the belief that her son did not commit a
gruesome murder, and yet, compatible with that inextinguishable belief,
she may be tortured by doubt.

A second kind of certainty is epistemic. Roughly
characterized, a belief is certain in this sense when it has the
highest possible epistemic status. Epistemic certainty is often
accompanied by psychological certainty, but it need not be. It is
possible that a subject may have a belief that enjoys the highest
possible epistemic status and yet be unaware that it does. (More
generally, a subject's being certain that p does not
entail that she is certain that she is certain that p; on this
point, see Van Cleve 1979, and see Alston 1980 on level confusions in
epistemology.) In such a case, the subject may feel less than the
full confidence that her epistemic position warrants. I will say
more below about the analysis of epistemic certainty and its relation
to psychological certainty.

Some philosophers also make use of the notion of moral
certainty (see Markie 1986). For example, in the Latin version of
Part IV of the Principles of Philosophy, Descartes says that
“some things are considered as morally certain, that is, as
having sufficient certainty for application to ordinary life, even
though they may be uncertain in relation to the absolute power of
God” (PW 1, pp. 289-90). Thus characterized, moral
certainty appears to be epistemic in nature, though it is a lesser
status than epistemic certainty. In the French version of this
passage, however, Descartes says that “moral certainty is
certainty which is sufficient to regulate our behaviour, or which
measures up to the certainty we have on matters relating to the conduct
of life which we never normally doubt, though we know that it is
possible, absolutely speaking, that they may be false” (PW 1, p.
289 n. 2). Understood in this way, it does not appear to be a
species of knowledge, given that a belief can be morally certain and
yet false (contra Markie 1986, p. 36). Rather, on this view, for
a belief to be morally certain is for it to be subjectively rational to
a high degree.

Although all three kinds of certainty are philosophically
interesting, it is epistemic certainty that has traditionally been of
central importance. In what follows, then, I shall focus mainly
on this kind of certainty.

There have been many different conceptions of certainty. Each
of them captures some central part of our intuitive understanding of
certainty, but, as we shall see, none of them is free from
problems.

Certainty is often explicated in terms of
indubitability. This has been done in a variety of
ways. One prominent account of certainty is suggested by
Descartes's presentation of his famous Archimedean point, the
cogito (I am thinking, therefore I exist). In the Second
Meditation, Descartes reviews the extensive doubts of the First
Meditation before saying that even if “there is a deceiver of
supreme power and cunning who is deliberately and constantly deceiving
me,” still “he will never bring it about that I am nothing
so long as I am something” (PW 2, p. 17). Descartes then
concludes that the proposition that he himself exists is true whenever
he considers it. It is often thought that the cogito has
a unique epistemic status in virtue of its ability to resist even the
“hyperbolic” doubts raised in the First Meditation (see
Markie 1992 and Broughton 2002). However, even if Descartes took
this view of the certainty of the cogito, he did not accept
the general claim that certainty is grounded in indubitability.
In the Third Meditation, Descartes says that he is certain that he is a
thinking thing, and he explains the certainty of this “first item
of knowledge” (it is unclear whether he regards it as distinct
from the cogito) as resulting from the fact that it is a clear
and distinct perception (PW 2, p. 24). (Matters are complicated,
however, by the fact that Descartes also says in the Third Meditation
that certainty depends on knowing that God exists and is not a
deceiver.)

Ludwig Wittgenstein also seems to connect certainty with
indubitability. He says that “If you tried to doubt
everything you would not get as far as doubting anything. The
game of doubting itself presupposes certainty” (1969,
§115). What makes possible doubting is “the fact that
some propositions are exempt from doubt, are as it were like hinges on
which those turn” (1969, §341). Although
Wittgenstein's view is sometimes taken to be—or to provide
the basis for—an epistemically satisfying response to skepticism
(see, e.g., Wright 2003 and 2004), it is hard to see the kind of
certainty he has characterized as being epistemic, rather than merely
psychological, in nature (on this point, see Pritchard 2005).
Thus, when Wittgenstein says, “The difficulty is to realize the
groundlessness of our believing” (1969, §166) it seems clear
that the so-called hinge propositions are ones that we are
psychologically incapable of calling into question. This is, of
course, compatible with their being false.

In general, every indubitability account of certainty will face a
similar problem. The problem may be posed as a dilemma: when the
subject finds herself incapable of doubting one of her beliefs, either
she has good reasons for being incapable of doubting it, or she does
not. If she does not have good reasons for being unable to doubt
the belief, the type of certainty in question can be only
psychological, not epistemic, in nature. On the other hand, if
the subject does have good reasons for being unable to doubt the
belief, the belief may be epistemically certain. But, in this
case, what grounds the certainty of the belief will be the
subject's reasons for holding it, and not the fact that the
belief is indubitable.

A second problem for indubitability accounts of certainty is that,
in one sense, even beliefs that are epistemically certain can be
reasonably doubted. I shall say more about this in §3
below.

According to a second conception, a subject's belief is
certain just in case it could not have been
mistaken—i.e., false (see, e.g., Lewis 1929).
Alternatively, the subject's belief is certain when it is
guaranteed to be true. This is what Roderick Firth calls
the “truth-evaluating” sense of certainty (1967, pp.
7-8). As with knowing that p, being certain that
p entails that it is true that p. Certainty is,
however, significantly stronger than lesser forms of knowledge.
In cases where the subject knows without being certain that p,
it is actually true that p, though it could have been
false. But, where the subject is certain that p, it does
not merely turn out to be true that p—in some sense it
could not have been otherwise.

The difficulty for this conception of certainty is specifying the
precise sense in which the belief could not have been false. What
is meant cannot be what is called metaphysical or broadly logical
impossibility. Although some of the paradigmatically certain
beliefs are necessarily true in this sense, many others are not.
For example, though I am certain of the truth of the cogito,
it is not necessarily true (in the metaphysical sense) that I
exist. That is, it is possible that I might not have
existed. We might attempt to solve this difficulty by saying that
the belief is guaranteed to be true by the subject's grounds for
it (see, e.g., Audi 1998, pp. 218-9). But this opens up two
further problems for this conception of certainty. First, if the
truth of the belief is guaranteed by the subject's grounds for
holding it, then it looks as though the certainty of the belief ought
to be attributed to those grounds as well. That is to say, the
belief would be certain, not in virtue of the fact that it is
guaranteed to be true, but rather in virtue of its relation to the
grounds that make that guarantee possible. This would be so
because the grounds would provide a deeper explanation for the
certainty of the belief than would the fact that the belief is
guaranteed to be true.

The second problem is very similar to one that arises for
philosophers attempting to provide an account of fallibilistic
knowledge (i.e., knowledge that is less than certain). According
to the standard account, the subject has fallibilistic knowledge that
p when she knows that p on the basis of some
justification j, and yet the subject's belief could have
been false while still held on the basis of j (see, e.g.,
BonJour 1985, p. 26, and Lehrer 1990, p. 45). Alternatively, the
subject knows that p on the basis of some justification
j, but j does not entail the truth that p
(see, e.g., Cohen 1988, p. 91; Fogelin 1994, pp. 88-9; and Jeshion
2000, pp. 334-5). The problem with the standard account, in
either version, is that it does not allow for fallibilistic knowledge
of necessary truths. If it is necessarily true that p,
then the subject's belief that p could not have been
false, regardless of what her justification for it may be like.
And, if it is necessarily true that p, then
everything—including the subject's justification for her
belief—will entail or guarantee that p. Our
attempt to account for certainty encounters the opposite problem: it
does not allow for a subject to have a belief regarding a necessary
truth that does not count as certain. If the belief is
necessarily true, it cannot be false—even when the subject has
come to hold the belief for a very bad reason (say, as the result of
guessing or wishful thinking). And, given that the beliefs are
necessarily true, even these bad grounds for holding the belief will
entail or guarantee that it is true.

The best way to solve the problem for the analysis of fallibilistic
knowledge is to focus, not on the entailment relation, but rather on
the probabilistic relation holding between the subject's
justification and the proposition believed (see Reed 2002). When
the subject knows that p on the basis of justification
j, and P(p/j) is less than 1, the
subject's knowledge is fallibilistic. (Although
epistemologists will disagree about what the appropriate conception of
probability is, here is a crude example of how probability may figure
in a fallibilistic epistemology. A basic historical reliabilist
will say that a belief is justified just in case it has been produced
by a process that has yielded a preponderance of true beliefs.
So, if the process has yielded a true belief, say, 90% of the time, the
probability that the next belief will be true is 90%; this is so even
if the belief in question is necessarily true and has been logically
deduced from a set of beliefs, each of which is necessarily
true.) Adapting this solution to the problem for certainty, we
can say that the subject is certain that p when
P(p/j) = 1, where j is the
justification or grounds for the belief (see Van Cleve 1977 and Lewis
1952). However, in order for j to impart a probability
of 1 to p, it must also be the case that
P(j) = 1. That is to say, j must be
certain for the subject before it can make anything else certain.
But, if we are to explain the certainty that p by appeal to
the certainty that j, we fall into a vicious regress.
The only way to stop it is to allow that some beliefs may have an
intrinsic probability of 1 (see Russell 1948, p. 396, and Van Cleve
1977). It is, however, difficult to see how intrinsic probability
of this sort is possible (barring, of course, a subjectivist account of
probability, which could, in any case, capture only psychological
certainty).

According to a third conception of certainty, a subject's
belief that p is certain when it is justified in the highest
degree. This is what Firth calls the
“warrant-evaluating” sense of certainty (1967, pp.
8-12). Thus, Bertrand Russell says that “A proposition is
certain when it has the highest degree of credibility, either
intrinsically or as a result of argument” (1948, p. 396).
There are various ways to understand what it means for a belief to be
credible or justified in the highest degree. It could mean simply
that the belief in question is justified as highly as any belief the
subject happens to hold. But, in cases where the subject does not
have any beliefs that are highly justified, this will imply that even a
belief with relatively low justification is epistemically
certain. Perhaps we could say instead that a belief is justified
to the highest degree when it is justified as highly as any belief that
anyone happens to hold. But this, too, leaves open the
possibility that a belief with relatively low justification is
epistemically certain: if all the subjects in existence are in a
condition of universal ignorance, all of their beliefs—including
the best of them—will have only a low level of
justification. Perhaps, then, we should say that a belief is
justified in the highest degree when it has the highest level of
justification possible. But even this account is
unsatisfactory. Suppose that global skepticism is necessarily
true: it is a necessary truth that no subject is capable of having much
justification for any of her beliefs; although it may seem to us as
though a significant degree of justification is possible, this in fact
is incorrect. It would then be intuitively correct to say that
every belief falls far short of certainty, though this would not be
permitted by the account of certainty under consideration. We may
of course doubt that skepticism of this strong variety is correct;
nevertheless, it should not be simply ruled out as a matter of
definition.

Roderick Chisholm offers a variation on the above approach.
According to his first definition of certainty (where h,
S, and t are variables for propositions, subjects,
and times, respectively):

h is certain for S at t =df (i)
Accepting h is more reasonable for S at t
than withholding h (i.e., not accepting h and not
accepting not-h) and (ii) there is no i such that
accepting i is more reasonable for S at t
than accepting h. (1976, p. 27)

Clause (i) ensures that the subject has some measure of positive
justification for h—if she had no justification for it,
it would be more reasonable for her to withhold with respect to
h. Clause (ii) then says that those beliefs of the
subject are certain which are at the highest levels of justification
for her. However, this still leaves open the following
possibility: h is the most highly justified belief the subject
has, but it is still not very highly justified (e.g., it may not even
be sufficiently justified to count as knowledge).

Perhaps for this reason, Chisholm later offered a different
definition of certainty:

p is certain for S =df For every
q, believing p is more justified for S than
withholding q, and believing p is at least as
justified for S as is believing q. (1989,
p. 12)

This definition still has the equivalent of clause (ii) above, and
therefore requires the belief that is certain for the subject be the
one that is most highly justified for her. But the second
definition appears to be more successful in requiring that p
be justified to a significant degree. Now, believing that
p must not only be more justified for the subject than
withholding p, it must also be more justified than withholding
with respect to any other proposition. There are many
propositions that we are capable of entertaining—e.g., the
proposition that the number of people alive at this precise moment is
even—where there is not the slightest reason for thinking them to
be either true or false (though, of course, they must be one or the
other). In fact, given the perfect lack of evidence with respect
to propositions of this sort, Chisholm's definition may set the
standard for certainty too high, for it is hard to see how
there could be any proposition one is more justified in
believing than one is in withholding belief regarding, say, the parity
of the number of people alive at this very moment.

It should be noted, however, that Chisholm's definition works
only by implicitly relying on what is a contingent feature of our
epistemic situation. It so happens that we find ourselves in a
position of total ignorance with respect to some propositions.
But that need not have been the case. We could have ended up in a
world where there is a moderate amount of evidence either for or
against every proposition. If one of a subject's beliefs
then happened to have slightly more justification than any of the
others, it would meet Chisholm's definition of certainty, though
it might still have what we would intuitively take to be a less than
ideal level of justification.

There is one further problem with both of Chisholm's
definitions. Because they both relativize certainty to a
particular subject, they make possible the following situation.
Two subjects each believe that p, and in each case the
belief is justified to degree n. For the first subject,
the belief counts as certain because none of her other beliefs have a
higher level of justification. But, for the second subject, the
belief in question is not certain because she does have another belief
that is slightly more justified. If certainty really is grounded
in epistemic justification, though, this should not be possible.
If a given justification makes a belief certain for one subject, it
should do so for everyone.

There is another approach that Chisholm might take. According
to particularism, his favored method in epistemology, we
should use particular instances of knowledge and justification as our
guide in formulating an epistemology (Chisholm 1973 and 1989, pp.
6-7). (By contrast, methodism begins with criteria for
knowledge and justification and then attempts to ascertain whether, on
these criteria, we actually have any knowledge or justified
beliefs.) Adapting this approach to our present concern, the
suggestion is that we formulate an account of certainty in light of
paradigmatic instances of beliefs held with certainty. Thus,
after giving the second definition above, Chisholm says that the
concept of certainty is illustrated by propositions about what he calls
“self-presenting” mental states and by some logical and
metaphysical axioms (1989, p. 12).

Although this particularist approach probably is the way in which
most philosophers think of certainty, it faces several
difficulties. One is that the epistemology of the a
priori is far from clear. Given that we do not, apparently,
causally interact with necessary truths, it is hard to see how our
minds can have access to them. A second difficulty has to do with
knowledge of our own mental states—sometimes referred to as
knowledge by acquaintance. According to the
“speckled hen” problem, there are aspects of our mental
states, such as the rich detail of one's present visual
experience, that we are not capable of knowing—e.g., if one is
looking at a speckled hen, there will be a determinate number of
speckles in one's visual experience, which one will not be able
to know just in virtue of having the experience (Ayer 1940, Chisholm
1989, Fumerton 2005). But those aspects we cannot know merely by
being conscious of them are part of our conscious experience in just
the same way as those aspects we are supposed to be able to
know; the difficulty is specifying a principled difference between the
two. Much more could be said about the first two problems, but
they lie beyond the scope of this article. A third difficulty is
that, at least prima facie, knowledge of one's mental
states seems to be of a fairly different kind from knowledge of
necessary truths. It is not clear, at the outset, that we are
warranted in taking them to be paradigmatic instances of a genuine
epistemological kind.

According to a fourth conception of certainty, defended by Peter
Klein, a belief “is absolutely certain just in case it is
subjectively and objectively immune to doubt”
(1992, p. 63). He explicates this in the following way:

p is absolutely certain for S if and only if (1)
p is warranted for S and (2) S is warranted
in denying every proposition, g, such that if g is
added to S's beliefs, the warrant for p is
reduced (even if only very slightly) and (3) there is no true
proposition, d, such that if d is added to
S's true beliefs the warrant for p is reduced
(even if only very slightly). (1992, p. 63)

Klein says that the second condition is what makes the belief
subjectively immune to doubt, presumably because it is the beliefs and
experiences that constitute S's subjective perspective
that render her warranted in denying all propositions that would reduce
the warrant for p. However, S's belief
system might contain false beliefs that could warrant her in denying
every g relevant to p—even, in some cases,
where the g in question is itself true—and so her belief
that p might meet condition (2) and yet still be false.
Condition (3) is meant to prevent this situation; if p is
false, the true belief that ~p can be added to
S's belief system, thereby reducing the warrant
S has for p. In requiring both (2) and (3),
then, the account focuses on beliefs where the subject's
subjective situation is in a sense properly aligned with an objective
structure of reasons (for a similar view, see Pollock 1986).

There are two major difficulties facing a view of this sort.
First, it is not clear how one belief is supposed to reduce the warrant
for another. Suppose that I correctly believe that I have a
headache and that my belief is, in an intuitive sense, absolutely
certain. The first condition of Klein's account is
satisfied: the belief is warranted in virtue of my experiencing the
headache. But is the second condition also satisfied? That
is, would I be warranted in denying, say, the proposition that I do not
in fact have a headache? If this were to be a belief added to my
belief system, I would of course have contradictory beliefs.
Would that entail that the warrant for both beliefs should be
diminished? If the answer is yes, then my belief that I have a
headache is not absolutely certain. Moreover, it is hard to see
how any belief could then be absolutely certain, given that we
can always add to our belief systems the contradictory of any of our
beliefs. If the answer is no, however, there should be some
explanation for why the proposition that I do not have a headache can
be denied. Presumably, the explanation would have something to do
with my experiencing the headache. But then what explains the
certainty of the belief is the fact that it is grounded in the
experience; the belief's being subjectively immune to doubt is
merely a consequence of its certainty, and not the explanation for
it. This would mean that the focus of the view has shifted from
subjective immunity to doubt to some sort of special warrant. How
there could be such a special warrant, though, would need an
account. To see the point more clearly, notice that subjective
immunity to doubt will be possible only in cases where the
subject's belief is (intuitively) absolutely certain. For
any belief b that is less than certain, the following belief
could be added to the subject's belief system: the warrant for
b could be misleading. That belief would reduce the
subject's warrant for b (even if only slightly) were it
to be added to her belief system, but it is not a proposition the
subject can deny without being absolutely certain that b is
true. The upshot, then, is that subjective immunity to doubt is
not well-suited to playing a role in an account of certainty.
Instead, it looks as though our understanding of subjective immunity to
doubt depends on a prior grasp of what certainty is.

The second difficulty has to do with condition (3), which is
supposed to secure objective immunity to doubt. Although it is
undeniable that a subject for whom condition (3) is satisfied would be
in a desirable situation, it does not seem to be attributable to her in
the right sort of way—and, especially, not in the way that we
expect certainty to be attributable to the person who is certain.
To see this, suppose that my warrant for the belief that p is
only moderately good. Nevertheless, my guardian angel protects my
belief by making sure that any proposition such that, if it were true,
would (when added to my belief system) reduce my warrant for
p, is false. That is, my guardian angel makes sure that
all potential defeaters for my belief are removed. Suppose, for
example, that I see from a great distance what looks like a hawk.
My guardian angel immediately annihilates all non-hawk flying objects
in the area; the potential defeater, that there are flying objects
indistinguishable from a hawk in the vicinity, has thus been rendered
false. Although this would make my belief that p
objectively immune to doubt, insofar as (3) is satisfied, it does not
seem as though it would carry my belief any closer to certainty.
The fact that the warrant for my belief is only moderately good renders
irrelevant the work my guardian angel does in the world outside of my
beliefs. (Nor would the situation be helped if we stipulated that
condition (2) is also satisfied. Given that my belief system
could contain many false beliefs that might warrant me in rejecting all
potential defeaters, my belief might be both subjectively and
objectively immune to doubt—and yet still have a relatively low
degree of warrant.)

It may be that one of the four conceptions of certainty discussed
above could be improved so as to answer all objections. But,
until that happens, it is safe to say that there is at present no
completely satisfactory conception of certainty.

Typically, epistemologists are concerned with the conditions under
which a subject may know or be certain that p at a particular
moment. Interestingly, however, somewhat different issues arise
for certainty over time. As this was a primary concern for
Descartes, who tells us in the First Meditation that he wants to
establish something “in the sciences that was stable and likely
to last,” we can best see how those issues arise in the context
of Descartes's epistemology (PW 2, p. 12).

In the Second Set of Objections, Mersenne poses the following
problem: although Descartes has argued that our ability to know
anything depends on our first knowing that God exists and is not a
deceiver, it seems clear that an atheist mathematician can have the
same sort of mathematical knowledge as a theist. In response,
Descartes allows that the atheist does have a clear awareness
(cognitio) of simple mathematical truths, but he denies that
this clear awareness is “true knowledge
[scientia]” (PW 2, p. 101). At first glance, it
seems that Descartes draws the distinction between cognitio
and scientia precisely so he can deny certainty to the atheist
mathematician. But there is good reason to think that this is not
what he has in mind.

To see this, notice that, if Descartes does not allow the atheist to
be able to acquire knowledge through clear and distinct perception, he
will fall into the so-called Cartesian Circle. This problem,
first identified by Arnauld in the Fourth Set of Objections, arises if
Descartes holds both of the following claims: (i) I can know that my
clear and distinct perceptions are true only if I first know that a
non-deceiving God exists, and (ii) I can know that a non-deceiving God
exists only if I first know that my clear and distinct perceptions are
true. Because knowing one thing is a precondition for knowing the
other, and vice versa, I cannot know either of them. In
fact, however, it does not look as though Descartes does fall into the
circle. Although it is pretty clear that he is committed to
(1)—in the Third Meditation, he says that, “if I do not
know [whether there is a non-deceiving God], it seems that I can never
be quite certain about anything else” (PW 2, p. 25)—there
is no reason to take him to be committed to (ii). Descartes is
willing to permit the meditator to use clear and distinct perceptions
before knowing that they are generally true. The clearest
example, of course, is the cogito; the meditator first comes
to know that he exists as a thinking thing and only later comes to know
that his knowledge of the cogito is grounded in its clarity
and distinctness. The same, then, can be said for the
meditator's knowledge—grounded in some clearly and
distinctly perceived causal principles—that God exists. In
using those principles, the meditator does not first need to have the
general knowledge that clear and distinct perceptions are true (see Van
Cleve 1979).

Still, some philosophers might object that the meditator has no
business using principles that he does not know to be true. Descartes
would not be sympathetic to this objection. As he says in his
conversation with Burman, so long as the meditator is using the causal
principles, “he is actually paying attention to them. And for as
long as he does pay attention to them, he is certain that he is not
being deceived, and he is compelled to give his assent to them”
(PW 3, p. 334; see also PW 2, pp. 25, 48; see also Cottingham 1986,
p. 67). So, the doubt that Descartes raises with respect to clear and
distinct perceptions does not extend to the moments at which one is
actually enjoying them. Rather, it is a doubt that, in
general, clear and distinct perception may not be a reliable
source of beliefs (Kenny 1968, p. 194). When Descartes introduces the
evil demon hypothesis in the First Meditation, it is meant to
encapsulate his ignorance of his own origin—and, in particular,
ignorance of the construction of his own mind. Without knowing that a
non-deceiving God exists, it is possible for the meditator that his
mind works in such a way that it falls into error even when it is
contemplating the simplest questions. This doubt is chased away when
he actually does contemplate such a question, but it can
easily return at a later time when his thoughts are turned
elsewhere. This is the sense in which the atheist mathematician's
cognitio, or clear awareness, is imperfect. Although it is
certain at the time the atheist has the perception, it can always be
rendered doubtful at another time. The theist has no
advantage over the atheist at the time each enjoys a clear and
distinct perception. Rather, the theist's advantage lies in the fact
that, armed with the certainty that a non-deceiving God exists, she
will always remain free from doubt (Descartes PW 2, p. 48;
see also Kenny 1968, p. 193). Consequently, she will be able to
construct her scientific theories without ever falling prey to worries
about whether her work has value, and—perhaps even more
importantly—she will be in a position to definitively put an end
to theoretical disagreements with others. (The Stoics make a similar
distinction; see Cicero On Academic Scepticism, p. 84.)

Given this account of Descartes's epistemology, we can now see
that both cognitio and scientia are varieties of, not
only knowledge, but certainty as well. This is an important point
to note, for it means that certainty cannot be straightforwardly
characterized in terms of indubitability. For a belief known with
certainty to be immune to doubt—not merely at a moment but
absolutely—it must be embedded in a coherent system of beliefs,
all of which are known with certainty (for a similar account of
Descartes's epistemology, see Sosa 1997, though Sosa takes
cognitio to be a lower grade of knowledge than
scientia; also, see Loeb 1992 on the importance of stability
for Descartes's epistemology). Scientia, or
systematic certainty, represents an admirable, but probably
unattainable, goal. If humans are capable of certainty at all, it
is surely of the sort that is capable of mixing with doubts.

The SEP would like to congratulate the National Endowment for the Humanities on its 50th anniversary and express our indebtedness for the five generous grants it awarded our project from 1997 to 2007.
Readers who have benefited from the SEP are encouraged to examine the NEH’s anniversary page and, if inspired to do so, send a testimonial to neh50@neh.gov.